Digitized images require the storage and communication of large amounts of data. Medical imaging, graphics for games, military reconnaissance, space-based astronomy, and many other applications increasingly strain storage capacity and transmission bandwidth.
Although image compression techniques exist, some images, for example computerized tomography (CT) medical images require high resolution, high accuracy, and low contrast. Retrieval of these types of images must be lossless, or nearly so. Even less demanding applications are always open to further data compression.
A number of sources produce images in a transform domain, such as the frequency domain. For example, magnetic resonance imaging (MRI) scans, ultrasound scans, and computed tomography/microscopy devices output magnitude/phase data rather than spatial pixels to represent an image. Transform-domain images produce large amounts of data. For example, a spatial image 1000 pixels square, with 8-bit grayscale resolution requires one megabyte of data. A typical double-precision Fourier transform of that image produces about 16 MB of data: 8 MB for the magnitude component and 8 MB for the phase component. The frequency or magnitude component carries some of the information corresponding to the underlying spatial-domain image, and the complementary phase component carries the rest of the information. The ability to restore or reconstruct a spatial-domain image from only one of these transform-domain components could halve the bandwidth and/or time required to transmit the full image in either the spatial or transform domain. Storing only one component could reduce by 50% the space requirements on a disk or other medium. The U.S. Food and Drug Agency (FDA) requires that all medical source data has to be stored. Even when an image is generated initially in the spatial domain, it may be desirable to store or transmit the image in a transform-domain form.
Copending commonly assigned U.S. patent application Ser. No. 10/124,547, filed Apr. 17, 2002, demonstrates an iterative technique for restoring a spatial-domain image transmitted or stored as a single component of a transform-domain representation. Unlike previous such techniques, it requires no special conditions in the original image. However, being iterative, it requires processing time and capacity to pursue a number of iterations, making it hundreds or even thousands of times more computation intensive than a non-iterative or closed-form technique. Also, restoration is not lossless; the solution can only approach the pixel values of the original image more or less closely.